How Important Is Physics to a Mathematician?

[qspeechc]

I was just wondering about this, because I've heard it quite often that physics is fertile ground for new ideas in mathematics, historically and currently. In the past we can think of Newton inventing calculus to solve physics problems, Fourier inventing Fourier analysis (now that sounds odd; I doubt he named it after himself, but way to go if he did!)-- or what mathematicians today call Harmonic Analysis-- to solve engineering problems and so on. Today, I've often heard it said that particle physics, QFT, string theory etc. provide many ideas for research for mathematicians. How true is this?

How much physics should the mathematician and a mathematics student know? I am reading Peter Woit's book Not Even Wrong and he's convinced me phyics is very important to the research mathematician. Woit received his PhD in physics, but then moved to mathematics. I've also heard this opinion expressed a countless number of other times, from Witten, Atiyah (an admirer of Witten, btw), Bott, Hermann Weyl and many others, to pick on the famous people (I have forgetten most of the places I have heard this). Even in http://www.math.ohiou.edu/~shen/calculus/chen1.pdf" .

Most universities require math students to have at least a course in general physics, so appearently they think there is some worth in learning physics. How much should you know? I myself have taken courses in EM, QM and classical mechanics, but I have never seen anything I found usefull in any of my mathematics courses, since the only math that ever seems necessary is vector calculus and differential equations, not particularly interesting areas of mathematics in my opinion.

Any thoughts?

 

[mathman]

It depends very much on the career you want to pursue. If you want to go into applied math you need to know something about the area of application, such as physics, engineering, statistics, economics, etc. On the other hand you could use Hardy or Erdos as a model and just work in pure mathematics, presumably as a teacher.

 

[HallsofIvy]

To most mathematicians, physics is no more "important" than to any other person- which is a good reason for university students to take a physics course. But very very few research fields in mathematics have any connection to physics.

 

[qspeechc]

To most mathematicians, physics is no more "important" than to any other person- which is a good reason for university students to take a physics course. But very very few research fields in mathematics have any connection to physics.

That's not what Sir Michael Atiyah thinks:
http://www.wlap.org/umich/phys/colloq/2002/winter/atiyah/

Apparently Raoul Bott was influenced greatly by Edward Witten's work too.
http://www.crm.umontreal.ca/Bott08/index_e.shtml

Also check out:
www.pnas.org/content/85/22/8371.full.pdf
http://www.cgtp.duke.edu/

It seems that mainly geometry and topology have connections to modern physics.

 

[mathman]

It seems that mainly geometry and topology have connections to modern physics.

That is too narrow. Quantum theory relies heavily on probability theory. Group theory is important also in quantum theory. Calculus, diff. eq., complex variables, etc. are widely used also.

 

[Dragonfall]

I did not have to take a physics class when I was an undergrad. I probably wouldn't see much of a connection since I did a lot of discrete math (which is obviously the best field within mathematics).

 

[mathman]

I did not have to take a physics class when I was an undergrad. I probably wouldn't see much of a connection since I did a lot of discrete math (which is obviously the best field within mathematics).

Mathematicians do not need to learn any physics unless they want to do applied math in physics. Physicists, on the other hand, must have a good background in mathematics.

Why is discrete math the best field? To me, whatever your field is, it is a matter of taste more than anything else.

 

[Dragonfall]

Indeed it is a personal preference. I just like it very much.

 

[cmendnba]

I am a mathematician studying algebraic topology and I have no interest in physics. However, this is very subjective. One could argue that physics propells mathematical research. I disagree; in fact, I spend much of my time at work setting young physics and engineering students in the right path as far as the mathematics they are doing. But to do real mathematics, one doesn't need any knowledge of physics to be successful. The intuition one may think they have after doing some physics may even be a detriment. In practice, it is usually the case that the mathematics is developed first and only later are applications found by scientists.